准直伽马暴喷流余辉的动力学与光变曲线

Mandatory foundational reference for relativistic jets (R2). Step through the algebraic proof showing that post-break temporal steepening accelerates by $\Delta \alpha = 1$ due to lateral spread and geometry.

If GRBs are highly collimated into narrow cones, how does lateral relativistic expansion modify afterglow dynamics when beaming breaks down, and how can the geometric opening angle be measured empirically?

Proves that when the bulk Lorentz factor drops below the inverse jet half-angle $\Gamma(t) \sim 1/\theta_0$, relativistic beaming loss and sonic lateral expansion $$\theta(t) \sim \theta_0 + \frac{c_s}{c}\frac{1}{\Gamma(t)}$$ trigger exponential deceleration, producing an achromatic jet break in light curves.

• Initial jet structure is approximated as a top-hat cone with uniform opening half-angle $\theta_0$.
• Lateral expansion initiates when $\Gamma \theta_0 \sim 1$, driven outward by post-shock pressure at the sound speed $c_s = c/\sqrt{3}$.
• Ambient medium conforms to a uniform, constant-density interstellar environment.

Generalizes spherical blast waves to collimated relativistic jets with dynamic lateral expansion, resolving the GRB energy crisis by establishing the geometric beaming factor $f_b = 1 - \cos\theta_0$.